$24$ identical cells, each of internal resistance $0.5 \mathrm{\Omega }$, are arranged in a parallel combination of $n$ rows, each row containing $m$ cells in series. The combination is connected across a resistor of $3 \mathrm{\Omega }$. In order to send maximum current through the resistor, we should have

Two cells of emf $2E$ and $E$ with internal resistance $r_1$and $r_2$ respectively are connected in series to an external resistor $R$ (see figure). The value of $R,$ at which the potential difference across the terminals of the first cell becomes zero is

The variation of terminal potential difference $\left(V\right)$ with current flowing through as cell is as shown

The $\mathrm{emf}$ and internal resistance of the cell are

What is the time $t$ taken by the capacitor in the given circuit to charge to $\frac{1}{\sqrt{2\pi }}$ of its full capacity?

Six cells, each of emf $5\mathrm{V}$ and internal resistance $0.1\mathrm{\Omega }$ are connected as shown in Figure. The reading of the ideal voltmeter $\mathrm{V}$ is

In case two cells are identical, each of emf $E=5 \mathrm{V}$ and internal resistance $r=2 \Omega$, calculate the voltage across the external resistance $R=10 \Omega$

A student is asked to connect four cells of emf $\epsilon$each and internal resistance $\mathrm{r}$ in a series helping conditions. By mistake, he connects one cell in the opposite way. What will be the effective emf and effective internal resistance :

For the circuit shown in the figure, the current $I$ will be

In the given circuit, an ideal voltmeter connected across the $10 \mathrm{\Omega }$ resistance reads $2\mathrm{ }\mathrm{V}$ . The internal resistance $r$, of each cell is: